Problem: Is ${586436}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{5864} {36} = \gray{5864} \gray{00} + {36} $ Because $586400$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${36}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $36$ , divisible by $4$ Yes, ${36 \div 4 = 9}$, so $586436$ must also be divisible by $4$.